Highly Directional Small-Size Antenna Designed with Homogeneous Transformation Optics

Achieving high directivity antenna usually requires a large size antenna aperture in traditional antenna design. Previous work shows that, with the help of metamaterials and transformation optics, a small size antenna can perform as high directivity as a large size antenna, but the material parameters are inhomogeneous and difficult to realize. In this paper, we propose a linear homogeneous coordinate transformation to design the small size antenna. Distinguishing from inhomogeneous transformation, we construct a regular polygon in virtual space and then divide it into several triangle segments. By applying linear homogeneous coordinate transformation, the antenna devices can be greatly compressed without disturbing the radiation patterns by using homogeneous metamaterial substrates. The material parameters of the antenna designed from this method are homogeneous and easy to fabricate. Square and hexagonal antenna structures are numerically demonstrated to illustrate the validity of our methodology.